A microscopically motivated renormalization scheme for the MBL/ETH transition

Understand

We introduce a multi-scale diagonalization scheme to study the transition between the many-body localized and the ergodic phase in disordered quantum chains.

• The scheme assumes a sharp dichotomy between subsystems that behave as localized and resonant spots that obey the Eigenstate Thermalization Hypothesis (ETH).
• We establish a set of microscopic principles defining the diagonalization scheme, and use them to numerically study the transition in very large systems.
• To a large extent the results are in agreement with an analytically tractable mean-field analysis of the scheme: We find that at the critical point the system is almost surely localized in the thermodynamic limit, hosting a set of thermal inclusions whose sizes are power-law distributed.